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copied!<p>As the in-line comment goes, this is a simple "baseline trend algorithm", which basically means before you compare the trends of two different pages, you have to establish a baseline. In many cases, the mean value is used, it's straightforward if you plot the pageviews against the time axis. This method is widely used in monitoring water quality, air pollutants, etc. to detect any significant changes w.r.t the baseline.</p> <p>In OP's case, the slope of pageviews is weighted by the log of totalpageviews. This sorta uses the totalpageviews as a baseline correction for the slope. As Simon put it, this puts a balance between two pages with very different totalpageviews. For exmaple, A has a slope 500 over 1000,000 total pageviews, B is 1000 over 1,000. A log basically means 1000,000 is ONLY twice more important than 1,000 (rather than 1000 times). If you only consider the slope, A is less popular than B. But with a weight, now the measure of popularity of A is the same as B. I think it is quite intuitive: though A's pageviews is only 500 pageviews, but that's because it's saturating, you still gotta give it enough credit.</p> <p>As for the error, I believe it comes from the (relative) <a href="http://en.wikipedia.org/wiki/Standard_error_%28statistics%29" rel="noreferrer">standard error</a>, which has a factor 1/sqrt(n), where n is the number of data points. In the code, the error is equal to (1/sqrt(n))*(1/sqrt(mean)). It roughly translates into : the more data points, the more accurate the trend. I don't see it is an exact math formula, just a brute trend analysis algorithm, anyway the relative value is more important in this context.</p> <p>In summary, I believe it's just an empirical formula. More advanced topics can be found in some biostatistics textbooks (very similar to monitoring the breakout of a flu or the like.)</p>

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